Sojourn time analysis of a queueing system with two‐phase service and server vacations |
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| Authors: | Tsuyoshi Katayama Kaori Kobayashi |
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| Institution: | 1. Department of Electronics and Informatics, Toyama Prefectural University, Kosugi, Toyama 939‐0398, JapanDepartment of Electronics and Informatics, Toyama Prefectural University, Kosugi, Toyama 939‐0398, Japan;2. Department of Electronics and Informatics, Toyama Prefectural University, Kosugi, Toyama 939‐0398, Japan |
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| Abstract: | We consider a two‐phase service queueing system with batch Poisson arrivals and server vacations denoted by MX/G1‐G2/1. The first phase service is an exhaustive or a gated bulk service, and the second phase is given individually to the members of a batch. By a reduction to an MX/G/1 vacation system and applying the level‐crossing method to a workload process with two types of vacations, we obtain the Laplace–Stieltjes transform of the sojourn time distribution in the MX/G1‐G2/1 with single or multiple vacations. The decomposition expression is derived for the Laplace–Stieltjes transform of the sojourn time distribution, and the first two moments of the sojourn time are provided. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007 |
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| Keywords: | two‐phase service bulk service vacation system level‐crossing method |
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